Simple Math Question,.,PLs.,.help?

Question

Suppose that you have found two different solutions for a system of two linear equations. How many solutions must the system have??

Answer 1

well, if they are both linear equations, then there are 3 options, no solution, 1 solution or infinitely many solutions.

if there is no solution then the lines are paralell, if there is one solution then the lines have different slopes, and if you have found 2 solutions then you really have the 3rd case, infinitely many solutions, meaning the lines are right on top of each other.

hope this helps,

matttlocke

Answer 2

Lets say you have two linear equations of 3 variables each, this can have many solutions (in fact infinite number of solutions).

take 2x + 2y +z = 2
and x+y+z =1

if you subtract the second equation from the first, you get
x+y=1.

Looking at the above and the second equation, z=0. (since x+y=1 and x+y+z=1)

so any numbers that fit x+y=1 will be a solution to the above two linear equations (as long as z=0)

so one set of answer is x=.5, y =0.5, z=0
another set of answer is x=1,y=0,z=0.
etc etc.

You should learn about independent and dependent equation.

Answer 3

If you found two solutions for a system of two linear equations, then you have made an error on at least one of them.
If you plot the two equations on a graph, you will have two straight lines. The "solution" is where the two lines meet. Since they are straight lines, there is only one point (at most) where they meet.

Answer 4

Infinity.

If you have:
a1x + b1y = c1
a2x + b2y = c2

and a1 * b2 = a2 * b1

and c1 * a2 = a1 * c2

Then you have two equations representing the same line.

Answer 5

only can have one. cos both are straight lines. when straight line meets, there going to be one solution for both x and y axis.that means when you substitute for the value wrong.